Comparing Polynomial Functions: Determining Which Function Exceeds the Other

The video tutorial explains how to determine which of two polynomial functions eventually exceeds the other by comparing their degrees. It highlights the importance of the leading term in determining end behavior as x approaches infinity. Through visual examples and graphical analysis, it demonstrates that a polynomial with a higher degree will eventually surpass one with a lower degree, despite temporary leads by the latter. The tutorial concludes that the degree of the polynomial is the key factor in long-term dominance.

Explain why a polynomial with a higher degree will eventually outstrip one with a lower degree.

Describe the behavior of a cubic polynomial compared to a quadratic polynomial as x approaches infinity.

What is the significance of ignoring coefficients when comparing polynomial functions?